• Advances in nano research
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• v.16 no.5
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• pp.489-500
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• 2024

This paper studies the free vibration analysis of the piezo-magneto-thermo-elastic FG nanobeam submerged in a fluid environment. The problem governed by the partial differential equations is determined by refined higher-order State Space Strain Gradient Theory (SSSGT). Hamilton's principle is applied to discretize the differential equation and transform it into a coupled Euler-Lagrange equation. Furthermore, the equations are solved analytically using Navier's solution technique to form stiffness, damping, and mass matrices. Also, the effects of nonlocal ceramic and metal parts over various parameters such as temperature, Magnetic potential and electric voltage on the free vibration are interpreted graphically. A comparison with existing published findings is performed to showcase the precision of the results.

• Steel and Composite Structures
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• v.51 no.2
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• pp.103-116
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• 2024

Based on the consistent couple stress theory (CCST), we develop a unified formulation for analyzing the static bending and free vibration behaviors of functionally graded (FG) microscale beams (MBs). The strong forms of the CCST-based Euler-Bernoulli, Timoshenko, and Reddy beam theories, as well as the CCST-based sinusoidal, exponential, and hyperbolic shear deformation beam theories, can be obtained by assigning some specific shape functions of the shear deformations varying through the thickness direction of the FGMBs in the unified formulation. The above theories are thus included as special cases of the unified CCST. A comparative study between the results obtained using a variety of CCST-based beam theories and those obtained using their modified couple stress theory-based counterparts is carried out. The impacts of some essential factors on the deformation, stress, and natural frequency parameters of the FGMBs are examined, including the material length-scale parameter, the aspect ratio, and the material-property gradient index.

• Steel and Composite Structures
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• v.51 no.4
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• pp.407-416
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• 2024

The main objective of the present paper is to investigate the nonlinear vibration of buckled beams fixed at both ends and made of Aluminium allay (Al-alloy) reinforced with randomly dispersed Single Walled Carbon Nanotube (SWNT). The Mori-Tanak (M-T) micromechanical approach is selected to predict the homogenized material properties of the beams. The differential equation of motion governing the nonlinear behavior of the Euler-Bernoulli homogeneous beam is solved using an analytical method. The influences of diverse parameters including axial load, vibration amplitude, SWNT volume fraction, SWNT aspect ratio and beam slenderness ratio on the nonlinear frequency are studied.

• The Journal of the Korea institute of electronic communication sciences
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• v.18 no.6
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• pp.1009-1014
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• 2023

Comprehensive observations of the Euler method and the Lagrangian method were performed in order to obtain high-resolution observation data in space and time for the complex environment of new city. The two radiosondes, which measure meteorological parameters using Lagrangian methods, produced air pressure, wind speed and wind direction. They were generally consistent with each other even if the observation points or times were different. The temperature measured by the sensor exposed to the air during the day was relatively high as the altitude increased due to the influence of solar radiation. The temporal difference in wind direction and speed was found in the comparison of Euler's wind profiler data with radiosonde data. When the wind field is horizontally in homogeneous, this result implies the need to consider the advection component to compare the data of the two observation methods. In this study, a method of using observation data at different times for each altitude section depending on the observation period of the Euler method is proposed to effectively compare the data of the two observation methods.

• Korean Journal of Applied Biomechanics
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• v.15 no.4
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• pp.13-24
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• 2005

The purpose of this study was to compare kinematic data between experts and novices, and identify difference kinematic parameters changing direction to kick in penalty kick of soccer play. Novice subjects were 5 high school students Who has never been experienced a soccer player, and expert subjects were 5 competitive high school soccer players. The 3-d angle was calculated by Euler's Angle by inertial axis and local axis with three-dimensional cinematography. Kinematic parameters in this study consisted of angles of knee joints, hip joints, lower trunk and upper trunk when the support foot was contacted on ground and kicking foot impacted the ball. The difference of angle of knee joints in the flexion/extension was insignificantly showed below $4{\sim}9^{\circ}$ in groups and directions of ball at the time of support and impact. But the difference of angle of hip joint was significant in groups and directions of ball at the time of support and impact. Specially the right hip joint of experts were more flexed about $12^{\circ}$($43.99{\pm}6.17^{\circ}$ at left side, $31.87{\pm}4.49^{\circ}$ at right side), less abducted about $10^{\circ}$ ($-31.27{\pm}4.49^{\circ}$ at left side, $-41.97{\pm}6.67^{\circ}$ at right side) at impact when they kicked a ball to the left side of goalpost. The difference of amplitude angle in the trunk was significantly shown at upper trunk not lower trunk. The upper trunk was external rotated about $30^{\circ}$ (novice' angle was $-16.3{\pm}17.08^{\circ}$, expert's angle was $-43.73{\pm}12.79^{\circ}$) at impact. Therefore the significant difference of kinematic characteristics could be found at the right hip joint and the upper trunk at penalty kick depending on the direction of kicking.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.16 no.6
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• pp.2074-2093
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• 2022

RSA is known as one of the best techniques for securing secret information across an unsecured network. The private key which is one of private parameters is the aim for attackers. However, it is exceedingly impossible to derive this value without disclosing all unknown parameters. In fact, many methods to recover the private key were proposed, the performance of each algorithm is acceptable for the different cases. For example, Wiener's attack is extremely efficient when the private key is very small. On the other hand, Fermat's factoring can quickly break RSA when the difference between two large prime factors of the modulus is relatively small. In general, if all private parameters are not disclosed, attackers will be able to confirm that the private key is unquestionably inside the scope [3, n - 2], where n is the modulus. However, this scope has already been reduced by increasing the greatest lower bound to [d_il, n - 2], where d_il ≥ 3. The aim of this paper is to decrease the least upper bound to narrow the scope that the private key will remain within this boundary. After finishing the proposed method, the new scope of the private key can be allocated as [d_il, d_ir], where d_ir ≤ n - 2. In fact, if the private key is extremely close to the new greatest lower bound, it can be retrieved quickly by performing a brute force attack, in which d_ir is decreased until it is equal to the private key. The experimental results indicate that the proposed method is extremely effective when the difference between prime factors is close to each other and one of two following requirement holds: the first condition is that the multiplier of Euler totient function is very close to the public key's small value whereas the second condition is that the public key should be large whenever the multiplier is far enough.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.291-309
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• 2023

This paper addresses the finite element modeling of functionally graded porous (FGP) beams for free vibration and buckling behaviour cases. The formulated finite element is based on simple and efficient higher order shear deformation theory. The key feature of this formulation is that it deals with Euler-Bernoulli beam theory with only three unknowns without requiring any shear correction factor. In fact, the presented two-noded beam element has three degrees of freedom per node, and the discrete model guarantees the interelement continuity by using both C⁰ and C¹ continuities for the displacement field and its first derivative shape functions, respectively. The weak form of the governing equations is obtained from the Hamilton principle of FGP beams to generate the elementary stiffness, geometric, and mass matrices. By deploying the isoparametric coordinate system, the derived elementary matrices are computed using the Gauss quadrature rule. To overcome the shear-locking phenomenon, the reduced integration technique is used for the shear strain energy. Furthermore, the effect of porosity distribution patterns on the free vibration and buckling behaviours of porous functionally graded beams in various parameters is investigated. The obtained results extend and improve those predicted previously by alternative existing theories, in which significant parameters such as material distribution, geometrical configuration, boundary conditions, and porosity distributions are considered and discussed in detailed numerical comparisons. Determining the impacts of these parameters on natural frequencies and critical buckling loads play an essential role in the manufacturing process of such materials and their related mechanical modeling in aerospace, nuclear, civil, and other structures.

• Smart Structures and Systems
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• v.25 no.2
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• pp.219-228
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• 2020

This work presents a modified continuum model to explore and investigate static and vibration behaviors of perforated piezoelectric NEMS structure. The perforated nanostructure is modeled as a thin perforated nanobeam element with Euler-Bernoulli kinematic assumptions. A size scale effect is considered by included a nonlocal constitutive equation of Eringen in differential form. Modifications of geometrical parameters of perforated nanobeams are presented in simplified forms. To satisfy the Maxwell's equation, the distribution of electric potential for the piezoelectric nanobeam model is assumed to be varied as a combination of a cosine and linear functions. Hamilton's principle is exploited to develop mathematical governing equations. Modified numerical finite model is adopted to solve the equation of motion and equilibrium equation. The proposed model is validated with previous respectable work. Numerical investigations are presented to illustrate effects of the number of perforated holes, perforation size, nonlocal parameter, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric nanobeams.

• Wind and Structures
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• v.25 no.5
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• pp.459-474
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• 2017

In this study an analytical expression is derived for the natural frequency of the wind turbine towers supported on flexible foundation. The derivation is based on a Euler-Bernoulli beam model where the foundation is represented by a stiffness matrix. Previously the natural frequency of such a model is obtained from numerical or empirical method. The new expression is based on pure physical parameters and thus can be used for a quick assessment of the natural frequencies of both the real turbines and the small-scale models. Furthermore, a relationship between the diagonal and non-diagonal element in the stiffness matrix is introduced, so that the foundation stiffness can be obtained from either the p-y analysis or the loading test. The results of the proposed expression are compared with the measured frequencies of six real or model turbines reported in the literature. The comparison shows that the proposed analytical expression predicts the natural frequency with reasonable accuracy. For two of the model turbines, some errors were observed which might be attributed to the difference between the dynamic and static modulus of saturated soils. The proposed analytical solution is quite simple to use, and it is shown to be more reasonable than the analytical and the empirical formulas available in the literature.

• Advances in nano research
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• v.8 no.3
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• pp.255-264
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• 2020

Buckling and post-buckling cases are often occurred in aorta artery because it affected by higher pressure. Also, its stability has a vital importance to humans and animals. The loss of stability in arteries may lead to arterial tortuosity and kinking. In this paper, post-buckling analysis of aorta artery is investigated under axial compression loads on the basis of Euler-Bernoulli beam theory by using finite element method. It is known that post-buckling problems are geometrically nonlinear problems. In the geometrically nonlinear model, the Von Karman nonlinear kinematic relationship is employed. Two types of support conditions for the aorta artery are considered. The considered non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The aorta artery is modeled as a cylindrical tube with different average diameters. In the numerical results, the effects of the geometry parameters of aorta artery on the post-buckling case are investigated in detail. Nonlinear deflections and critical buckling loads are obtained and discussed on the post-buckling case.